calculus

sorry to ask a second question so soon, but i'm just not getting this one.

if f(x)= 3x lnx, then f'(x)=?

i used
f'(x)=3x(D lnx) + D (3x) (lnx)
f'(x)=3x (1/x) + 3 (lnx)
so... f'(x)=3+3lnx or 3(1+lnx).
unfortunately that isn't one of the possible answers given. could one of you kind folks help me understand where i went wrong?

thank you

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asked by ken
  1. I am getting the same answer.

    What are the other choices?

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    posted by Dr. Jane
  2. Wow! that was sooo fast. thank you for the help.
    sorry, i should have thought to provide the answers
    here they are.

    a) 3+ln(x^3)
    b) 1+ln(x^3)
    c) (3/x)+3lnx
    d) 3/(x^2)
    e) 1/x

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    posted by ken
  3. It is a. They used the law of logs or lns to rewrite 3 ln x as ln x^3.

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    posted by Dr. Jane
  4. Thank you very much. haven't touched this kind of stuff in a while. your help is much appreciated.

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    posted by ken
  5. You are welcome. So many times, students know the Calculus, but it is something from past math courses that cause the issue with finding the final answer.

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    posted by Dr. Jane

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